L’ Hospital’s Rule

We have dealt with problems which had indeterminate from either 0/0 or ∞/∞ .

The other indeterminate forms are ∞-∞,0,∞,00,∞0,1∞

We state below a rule, called L' Hospital's Rule, meant for problems on limit of the form 0/0 or ∞/∞ .

Let f(x) and g(x) be functions differentiable in the neighbourhood of the point a, except may be at the point a itself. If limx→a f(x) = 0 = limx→a g(x) or limx→af(x)= ∞ = ∞ g(x), then limx→a f(x)/g(x) = limx→a f' (x)/g(x) = limx→a f' (x)/g'(x) provided that the limit on the right either exists as a finite number or is ± ∞ .